Fuzzy Control and Modeling Techniques Based on Multidimensional Membership Functions Defined by Fuzzy Clustering Algorithms

The increasing complexity of nonlinear multivariable systems poses significant challenges for effective modeling and control. Fuzzy modeling and control typically use fuzzy inference with one-dimensional membership functions. However, the use of multidimensional membership functions can provide significant benefits in optimizing and reducing the computational cost of a fuzzy controller. In this work, we propose the use of fuzzy clustering techniques to adjust and design multidimensional membership functions. These techniques represent a well-developed and comprehensive framework, though they are often disconnected from traditional fuzzy modeling and control methodologies. Thus, this work also seeks to combine fuzzy techniques of different applications with a single ultimate goal, namely, to optimize the modeling and control of nonlinear systems. Our main objective is system identification, modeling, and control using the Takagi–Sugeno method based on one-dimensional and multidimensional membership functions. Moreover, a comparison of various fuzzy clustering techniques for the design of multidimensional membership functions is carried out to demonstrate the effectiveness of the proposed methods in optimizing control performance and reducing computational cost.